Using depth in three-dimensional object printing to form colors that change with viewing and illumination angles

ABSTRACT

A three-dimensionally printed object includes a plurality of different material regions that together define a surface region of the object. The plurality of different material regions includes a first material region and a second material region. The first material region has a first color, and the second material region has a second color that is different from the first color. The different material regions overlap from each other within the object by different amounts viewed from different directions so that different proportions of light from the plurality of different material regions are visible to an observer viewing the surface region of the three-dimensionally printed object from different view directions, different view angles, and with illumination lighting the surface region at different angles. A coloration of the surface region is altered based on the proportions of light from the plurality of different material regions visible to the observer.

TECHNICAL FIELD

This disclosure relates generally to three-dimensional object printing,and, in particular, to printing three-dimensional objects with colorsthat change based on viewing and illumination angles and directions.

BACKGROUND

Various techniques have been used to form objects with iridescentsurfaces, i.e., a surface that appears to change color as the angle ofview or the angle of illumination of the surface changes. In oneexample, a diffraction grating disposed on a surface is used to reflector transmit different portions of incident light. The different lightportions are seen as a view of an image that changes as the angle ofincidence changes. In another example, multiple images are separatedinto strips, interlaced with each other on a surface, and overlaid withlenticular lenses. The lenses are aligned with the interlacing of theimages so that light from each individual image is sent in a samerespective direction. This configuration reveals different images to anobserver over different view angles. In a further example, regions of asurface are embossed to have a periodic variation in a respectivedirection. The regions are colored with variations aligned with theperiodic variation to enable a change in viewing angle to hide, subdue,or highlight one or more of the colors.

Known techniques of forming an iridescent surface on an object, such asthe foregoing examples, generally consist of regions that only changecolor over a single view axis. For example, an image may change as anobserver's view is shifted left-right, but does not change when the viewis shifted up-down, or toward-away, or when the view is rotated. Inanother example, some iridescent paints, such as pearlescent paints,change color based on view angle, but change in the same mannerregardless of view direction. Additionally, iridescent surfacestypically require a structured surface, e.g., a diffraction grating,lenticular lenses, or embossed ridges, or are limited in terms of whatcolor changes are available. These structured surfaces increase theexpense and complexity of forming an iridescent surface, and result in asurface that is susceptible to damage that can interfere with theintended coloration of the surface. Additionally, such structures areimpractical or impossible to form on a three-dimensional printed objectthat has a non-planar or irregular shape that changes color along morethan one axis.

Digital three-dimensional object manufacturing, also known as digitaladditive manufacturing, is a process of making a three-dimensional solidobject of virtually any shape from a digital model. Three-dimensionalobject printing is an additive process in which successive layers ofmaterial are formed on a substrate in different shapes. The layers canbe formed by ejecting binder material, directed energy deposition,extruding material, ejecting material, fusing powder beds, laminatingsheets, or exposing liquid photopolymer material to a curing radiation.The substrate on which the layers are formed is supported either on aplatform that can be moved three dimensionally by operation of actuatorsoperatively connected to the platform, or the material depositiondevices are operatively connected to one or more actuators forcontrolled movement of the deposition devices to produce the layers thatform the object. Three-dimensional object printing is distinguishablefrom traditional object-forming techniques, which mostly rely on theremoval of material from a work piece by a subtractive process, such ascutting or drilling.

Techniques have also been developed for coloring the surface ofthree-dimensional printed objects that include applying coloration afteran object has been printed, and printing an object from differentmaterials having different colors. However, three-dimensional printinghas not been adapted to forming iridescent objects. Therefore, additivemanufacturing processes that produce three-dimensional objects withsurfaces having a coloration that changes when viewed at differentangles and directions and illuminated with light from different angleswould be beneficial.

SUMMARY

To facilitate the three-dimensional printing of objects withiridescence, in particular iridescent three-dimensional objects havingirregular shapes and surfaces, a three-dimensional object according tothis disclosure includes a plurality of different material regions thattogether define a surface region of the three-dimensionally printedobject. The plurality of different regions includes a first materialregion having a first color and a second material region having a secondcolor that is different from the first color. The different materialregions overlap each other by different amounts viewed from differentdirections to enable different proportions of light from the pluralityof different material regions to be visible to an observer viewing thesurface region of the three-dimensionally printed object from differentview directions, different view angles, and with illumination lightingthe surface region at different angles. The arrangement of the pluralityof different material regions also enables a coloration of the surfaceregion of the three-dimensionally printed object to be altered based onthe proportions of light from the plurality of different materialregions visible to an observer.

An exemplary system according to this disclosure is configured to modifythree-dimensional data for printing a three-dimensional object so thatthe three-dimensional object has a surface region having different colorarrangements visible to an observer viewing the surface region fromdifferent view directions, different view angles, and with illuminationlighting the surface region at different angles. The system includes amemory, an input device, a processor, and an output device.Three-dimensional data for operating a printer to print athree-dimensional object is stored in the memory. The input device isconfigured to receive data corresponding to at least two different colorarrangements for the surface region of the three-dimensional object, anddata corresponding to at least one of a view direction, a view angle,and an illumination angle assigned to each different color arrangement.The processor is configured with programmed instructions stored in thememory that enable the processor to modify the three-dimensional data tooperate a three-dimensional object printer to form the three-dimensionalobject with different color arrangements visible to an observer viewingthe surface region from different view directions, different viewangles, and with illumination lighting the surface region at differentangles. The processor is thereby configured to generate a color changemap for the surface region of the three-dimensional object withreference to a portion of the three-dimensional data corresponding to ageometry of the surface region of the three-dimensional object, the datareceived by the input device that corresponds to at least two differentcolor arrangements for the surface region, and the data received by theinput device that corresponds to the at least one of the view direction,the view angle, and the illumination angle assigned to each differentcolor arrangement. The processor generates a model of thethree-dimensional object that includes data corresponding to a pluralityof different material regions that together define a model surfaceregion of the model and that overlap by different amounts viewed fromdifferent directions to enable identification of different proportionsof light from the different material regions that are visible to anobserver viewing the model surface region from different view angles,different view directions, and with illumination lighting the modelsurface region at different angles. The processer simulates a view of anobserver viewing the model surface region with reference to the datacorresponding to the at least one of the view direction, the view angle,and the illumination angle assigned to each different color arrangementand identifies different proportions of light from the differentmaterial regions that are visible to the observer from the at least oneof the view direction, the view angle, and the illumination angleassigned to each different color arrangement with reference to thesimulated view of the observer. The processor generates a color changemap of the model surface region with reference to the identifiedproportions of light from each material region visible to the observerand compares the generated color change map of the model surface regionto the generated color change map for the surface region of thethree-dimensional object to measure a similarity of at least one ofcolor hue and color location between the generated color change map ofthe model surface region and the generated color change map of thesurface region of the three-dimensional object. The processor generatesthe model of the three-dimensional object in response to the measuredsimilarity being less than a predetermined threshold at the at least oneof the assigned view direction, view angle, and illumination angle, andcontinues the simulation of the observer viewing the model surfaceregion, the identification of the proportions of light, the generationof the color change map of the model surface region, the comparison ofthe generated color change map of the model surface region to thegenerated color change map for the surface region of thethree-dimensional object, and the generation of the model of thethree-dimensional object with reference to the measured similarity untilthe measured similarity between the generated color change map for thesurface region of the three-dimensional object and the generated colorchange map of the model surface region is greater than the predeterminedthreshold at the at least one of the assigned view direction, viewangle, and illumination angle. Once the measured similarity is greaterthan the predetermined threshold, the processor modifies thethree-dimensional data for printing the three-dimensional object withreference to the generated model of the three-dimensional object thathad the measured similarity that was greater than the predeterminedthreshold at the at least one of the assigned view direction, viewangle, and illumination angle, and transmits the modifiedthree-dimensional data to the three-dimensional object printer to enablethe printer to produce the three-dimensional object with the surfaceregion having the at least two different color arrangements visible toan observer viewing the surface region from the at least one of viewdirection, view angle, and illumination angle assigned to each differentcolor arrangement.

An exemplary method for operating a three-dimensional object printer toprint an iridescent three-dimensional object according to thisdisclosure includes operating a plurality of ejectors of thethree-dimensional printer with a controller to form a plurality ofdifferent material regions that together define a surface region of thethree-dimensionally printed object. The operating of the ejectors toform the plurality of different material regions includes operating afirst subset of the plurality of ejectors that eject drops of a materialhaving a first color to form a first material region of the first color,and operating a second subset of the plurality of ejectors that ejectdrops of a material having a second color that is different than thefirst color to form a second material region of the second color. Theplurality of different material regions overlap each other by differentamounts viewed from different directions to enable different proportionsof light from the plurality of different material regions to be visibleto an observer viewing the surface region of the three-dimensionallyprinted object from different view directions, different view angles,and with illumination lighting the surface region at different angles.The arrangement of the plurality of the different material regions alsoenables a coloration of the surface region of the three-dimensionallyprinted object to be altered based on the proportions of light the firstmaterial region and second material region visible to the observer.

BRIEF DESCRIPTION OF THE DRAWINGS

The foregoing aspects and other features of the present disclosure areexplained in the following description, taken in connection with theaccompanying drawings.

FIGS. 1-5 are side cross-section views of different exemplaryembodiments of three-dimensionally printed objects with surfaces havingan apparent coloration that changes over different view angles, viewdirections, and illumination angles according to this disclosure.

FIG. 6 is a top view of several different exemplary embodiments ofarrangements of material regions having apparent colorations that changegiven different view angles, view directions, and illumination anglesalong at least two different axes, according to this disclosure.

FIGS. 7A-8 are side cross-section views of further different exemplaryembodiments of three-dimensionally printed objects with surfaces havingan apparent coloration that changes over different view angles, viewdirections, and illumination angles according to this disclosure.

FIG. 9A is a side cross-section view of an exemplary embodiment of anirregular three-dimensionally printed object with a surface having anapparent coloration that changes over different view angles, viewdirections, and illumination angles according to this disclosure.

FIG. 9B is a schematic illustration of different images visible on thesurface of a three-dimensionally printed object at different viewangles, view directions, and illumination angles according to thisdisclosure.

FIG. 9C is a cross-section detail view of the three-dimensionallyprinted object of FIG. 9B.

FIG. 10A is a flow diagram of an exemplary embodiment of a method forproducing a three-dimensional object with a surface region that hasdifferent color arrangements visible to an observer viewing the surfaceregion from different view directions, different view angles, and withillumination lighting the surface region at different angles, accordingto this disclosure.

FIG. 10B is a schematic of an exemplary embodiment of a systemconfigured to perform the method of FIG. 10A.

FIG. 11 is a schematic of an exemplary embodiment of a three-dimensionalobject printer for printing a three-dimensional object according to thisdisclosure.

DETAILED DESCRIPTION

For a general understanding of the present embodiments, reference ismade to the drawings. In the drawings, like reference numerals have beenused throughout to designate like elements.

FIG. 1 illustrates a side cross section view of an exemplary embodimentof a three-dimensional object 100 according to this disclosure. Theobject 100 includes first material regions 104, second material regions106, a third material region 108, a fourth material region 110, and afifth material region 112. The material regions 104-112 are collectivelyreferred to as a plurality of material regions 102. The fifth materialregion encapsulates the remainder of the material regions 102, which areassembled into various arrangements 116, 122, and 124. Each arrangement116, 122, and 124 includes at least two different material regionshaving different colors, as described in more detail below. Thearrangements 116, 122, and 124 are spaced apart from each other byportions of the fifth material region.

The fifth material region 112 defines a surface region 114 of the object100, and is at least partially transparent such that the variousarrangements 116, 122, and 124 are at least partially visible through asurface 115 of the surface region 114. The remaining material regions102 overlap each other by different amounts viewed from differentdirections to enable different proportions of light from the pluralityof different material regions 102 to be visible to an observer viewingthe surface region 114 of the three-dimensionally printed object 100from different view directions, different view angles, and withillumination lighting the surface region at different angles. In thisembodiment, the first material regions 104 are magenta, the secondmaterial regions 106 are cyan, the third material region 108 is yellow,and the fourth material region 110 is black, but other colorations andcombinations of colorations are also contemplated.

In each of the arrangements 116, a first material region 104 and asecond material region 106 are at different distances from the surface115, the first material region 104 being closer to the surface 115 thanthe second material region 106. Due to this configuration, differentportions of the first material region 104 and second material region 106are visible to an observer viewing the surface region 114 at differentview angles.

In this disclosure, various observers are described as viewing thesurface regions of various objects. The reader should understand thatthe figures are not drawn to scale. Specifically, in FIG. 1 theplurality of material regions 102 are sized and arranged such that aleast a portion of the sides of the various arrangements 116, 122, and124 are visible to an observer viewing the surface region 114 at anoblique angle. Furthermore, unless otherwise stated, the variousobservers are viewing the objects under general diffuse light thatilluminates the surface region of the object.

A first observer 118 in FIG. 1 is viewing the surface region 114 at agenerally vertical angle, i.e., about 90 degrees relative to the surfaceregion 114. From the perspective of the first observer 118, at least aportion of the second material region 106 in the arrangement 116 isobstructed from view by the first material region 104. Thus, from theperspective of the first observer 118, the apparent coloration ofsurface region 114 of the object 100 is generally magenta.

In comparison, a second observer 120 is viewing the surface region 114at an oblique angle, i.e., an angle other than 90 degrees and 0 degrees.From the perspective of the second observer 120, at least a portion ofthe second material region 106 is visible beneath the first materialregion 104 in the arrangements 116. Since the second material region 106is cyan, the apparent coloration of the surface region 114 from theperspective of the second observer 120 is a mixture of magenta from thefirst material region 104 with cyan from the second material region 106.The magenta and cyan are mixed in proportion to the portion of thesecond material region 106 visible relative to the portion of the firstmaterial region 104 visible in the arrangement 116. Thus, for a mostlyvertical angle where only a small portion of the second material region106 is visible, the apparent coloration of the surface region isgenerally magenta, but as the view angle becomes more oblique, a largerportion of the second material region 106 becomes visible to the secondobserver 120 and the apparent coloration of the surface 115 of thearrangement 116 changes toward blue, a mixture of cyan and magenta.

To form a larger portion of the surface region 114 having a consistentcoloration behavior, multiple arrangements 116 are repeated next to eachother. From the perspective of the observers 118 and 120, the repeatedarrangements blend together and to present the appearance of a singlecoloration region. In this manner large regions of similar colorationcan be formed regardless of a size of the individual material regions.

In arrangement 122, the third material region 108 is beneath the firstmaterial region 104 with reference to the surface 115. From theperspective of the first observer 118, the third material region 108 isobstructed from view by the first material region 104, and thus theapparent coloration of surface region 114 of the object at thearrangement 122 appears generally magenta similar to the surface region114 at the arrangements 116. However, as the view angle becomes moreoblique, a larger proportion of light from the third material region 108becomes visible. Thus, from the perspective of the second observer 120,the apparent coloration of the surface region 114 shifts toward red dueto the magenta from the first material region 104 mixing with the yellowfrom the third material region 108.

In arrangement 124, a second material region 106 is beneath the fourthmaterial region 110 with reference to the surface 115. From theperspective of the first observer 118, the surface region 114 has ablack coloration portion at the arrangement 124 due to the black fromthe fourth material region 110, and from the perspective of the secondobserver 120, the surface region has darkened cyan coloration portionfrom a mixture of the black from the fourth material region 110 and thecyan from the second material region 106. In this embodiment, the fifthmaterial region 112 encapsulates the remaining material regions suchthat at least a portion of the fifth material region 112 is disposedbetween the remaining material regions 102 and the surface region 114.This portion of the fifth material region 112 can be configured as aprotective coating that protects the remaining material regions fromdamage, abrasion, scratches, or the like.

Varying the material regions included in arrangements within the object100, as with the arrangements 116, 122, and 124, enables the formationof different colorations of the surface region 114 at different viewangles. Since FIG. 1 is a side cross section view, the reader shouldunderstand that the distribution of arrangements of the material regions102 may extend over three dimensions. Thus, the arrangement of thematerial regions 102 can be used to form different images on the surface115 that are visible at different view angles.

Additionally, although the spacing, size, and positioning of thematerial regions 102 in FIG. 1 are illustrated as being generallyregular, the size, shape, and spacing of the material regions may bevaried. The shape and size of a material region is related to theangular range in which that material region is visible, and the spacingand relative sizing between regions relates to the color mixing betweenmaterial regions due to the portions of the overlapping material regionsviewable at various angles. Thus, adjusting the shape, size, and spacingof the material regions can alter the color change behavior of thesurface region 114 of the object 100.

The size of the material regions 102 may also be related to an intendedview distance for an observer. In one embodiment, the material regions102 are sized such that an observer viewing the surface region 114 ofthe object 100 from a predetermined distance perceives the plurality ofmaterial regions 102 as forming an unbroken coloration on the surface115. Individual material regions can be sized on the order ofcentimeters, millimeters, tens of micrometers, or less.

FIG. 2 illustrates another exemplary embodiment of a three-dimensionalobject 200 according to this disclosure. The object 200 includes anarrangement 201 having a first material region 204, a second materialregion 206, a fourth material region 210 and a fifth material region212. The arrangements 201 are separated from one another andencapsulated by a fourth material region 208 that defines a surfaceregion 214 of the object 200. The material regions 204-212 arecollectively referred to as a plurality of regions 202. In thisembodiment, the first material region 204 is magenta, and the secondmaterial region 206 is cyan, but other color combinations are alsocontemplated. The third material region 208 is at least partiallytransparent, the fourth material region 210 is white, and the fifthmaterial region 212 is black.

The second material region 206 and the first material region 204 are atdifferent distances from a surface 215 of the surface region 214, withthe first material region 204 being closer to the surface 215. At leasta portion of the transparent third material region 208 is disposedbetween the first material region 204 and second material region 206with reference to the surface 215. This configuration enables a largerproportion of light from the second material region 206 to be visiblefrom various view angles relative to the proportion of light from secondmaterial regions 106 visible at various angles in the embodimentillustrated in FIG. 1.

In some embodiments, one or more of the material regions 202 may not becompletely opaque. The degree of translucence may result in undesiredbleed-through of the color of material regions that are desirablyobstructed from view, which can affect the apparent coloration of thesurface region 214 of the object. In this embodiment, the white fourthmaterial region 210 acts as a buffer or scattering material to inhibitbleed-through. The fourth material region 210 is disposed between thefirst material region 204 and the second material region 206 relative tothe surface 215. Colored light that would otherwise be transmitted isinstead scattered within the fourth material region 210 to inhibit cyanlight from the second material region 206 from transmitting through thefirst material region 204.

In some embodiments, the third material region 208 may not be completelytransparent so light passing through the region is scattered to somedegree. Scattering may result in colored light being visible on thesurface region 214 from undesired view angles. For example, some amountof light reflected from or transmitted from the cyan second materialregion 206 may scatter within the third material region 208. Even thoughthe second material region 206 is obstructed from view by the firstmaterial region 204 from the perspective of the first observer 216, aportion of scattered cyan light from the second material region 206 mayexit the surface region 214 in a manner visible to the first observer216.

In the embodiment of FIG. 2, the fifth material region 212 acts as ascatter guard that inhibits the scattering of light within the thirdmaterial region 208 being visible in the region of the scatter guard. Inthis embodiment, the fifth material region 212 is black, but othermaterial regions of other colors can also be used as a scatter guard inother embodiments. Light that would otherwise be scattered through thethird material region 208 in a vicinity of the first material region 204is instead absorbed or blocked by the scatter guard. In this way, thecoloration of the surface region from the perspective of the firstobserver 216 is not distorted by scattered light from obstructedmaterial regions. In another embodiment (not shown), a scatter guardmaterial region is disposed to at least partially surround the secondmaterial regions 206.

As illustrated in FIG. 2, the fourth material region 210 and fifthmaterial region 212 are thinner than the first material region 204 andsecond material region 206. This difference in thickness reduces thecontribution of the white and black colors from the fourth materialregion 210 and fifth material region 212, respectively, on the apparentcoloration of the surface region 214 as seen by the second observer 218.

FIG. 3 illustrates a further exemplary embodiment of a three-dimensionalobject 300 according to this disclosure. The object 300 includes a firstplurality of material regions 202 that are similar to the plurality ofregions discussed above with regard to FIG. 2. The object furtherincludes a plurality of material regions 302 that define another surfaceregion 314 and a base 330 disposed between the first material regions202 and the second material regions 302. In this embodiment, the base330 is white and acts as a buffer to inhibit bleed-through between thefirst material regions 202 and the second material regions 302. Thisbuffer enables the surface regions 214 and 314 of the three-dimensionalobject 300 to have different coloration behaviors that do not interferewith each other. Although the base 330 is white in this embodiment,bases of other colors and of combinations of colors are alsocontemplated. Additionally, although the base 330 illustrated in FIG. 3is a generally planar member, other configurations are alsocontemplated. For example, the base 330 can have irregular surfaceregions and can have any three-dimensional shape.

FIG. 4A illustrates a further embodiment of a three-dimensional object400 according to this disclosure. The object 400 includes arrangements414 that each include a first material region 406 and a second materialregion 408. The object 400 also includes transparent material regions412 disposed between the arrangements 414 and a base 410 that supportsthe arrangements 414 and the transparent material regions 412. Thematerial regions 406, 408, and 412 are collectively referred to as aplurality of material regions 402. Unlike the embodiments illustrated inFIGS. 1-3, a surface 405 of the surface region 404 is not defined solelyby the transparent material region 412. Instead, the surface 405 isdefined by the first material regions 406 and second material regions408 together with the transparent material regions 412.

In this embodiment, the first material region 406 is yellow, and thesecond material region is cyan, but other color combinations are alsocontemplated in other embodiments. In each arrangement 414, the firstmaterial region 406 overlaps with the second material region 408 in adirection generally parallel to the surface 405. As discussed below,this configuration enables different apparent colorations of the surfaceregion 404 from different view directions.

From the perspective of a first observer 418 viewing the surface region404 from a first view direction 419, a larger proportion of light fromthe first material region 406 is visible than of the second materialregion 408 since at least a portion of the second material region 408 isobstructed from view by the first material region 406. In other words,while only a top surface region of the second material region 408 facingthe surface 405 is visible to the first observer 418, both the topportion of the first material region 406 facing the surface 405 and aside portion visible through a transparent material region 412 arevisible. Thus, from the perspective of the first observer 418, theapparent coloration of the surface region 404 is generally yellow. Fromthe perspective of a second observer 420 viewing the surface region 404from a second view direction 421, a larger proportion of light from thesecond material region 408 is visible than of the first material region406. From the perspective of the second observer 420, however, theapparent coloration of the surface region 404 is generally cyan.Additionally, as the view angle of an observer approaches 90 degreesfrom either view direction, the apparent coloration of the surfaceregion 404 shifts toward green due to the generally equal visibleproportions of light from the first material region 406 and secondmaterial region 408 so the cyan and yellow lights mix together. If thefirst material regions 406 and second material regions 408 are at leastpartially transparent, colored light from one of the colored materialregions may bleed through to the other. Additionally, if the transparentmaterial region 412 is not sufficiently transparent, colored light fromthe first and second material regions 406 and 408 may at least partiallyscatter and be visible from undesirable view angles.

FIG. 4B illustrates another exemplary embodiment of a three-dimensionalobject 428 that is similar to the object 400 illustrated in FIG. 4A, butadditionally includes buffers 430 and scatter guards 432. The buffers430 are disposed between the first material regions 406 and the secondmaterial regions 408 in each arrangement 414, and are configured toinhibit bleed-through of light from one colored material region to theother. In this embodiment, the buffers 430 are white, but buffers ofother colors are also contemplated. Additionally, in this embodiment,the buffers 430 are narrow compared to the first and second materialregions 406 and 408. A narrower buffer 430 can limit the impact of thecolor of the buffer 430 on the coloration of the surface region 404 ofthe object 428.

The scatter guards 432 are disposed within the transparent materialregions 412 between the arrangements 414 of the first and secondmaterial regions 406 and 408, and are configured to limit an amount ofscattering that occurs within the transparent material regions 412. Inthis embodiment, the scatter guards 432 are white so as to be a samecolor as the base 410. Having a scatter guard 432 with a same color asthe base 410 can limit the impact of the color of the scatter guard 432on the coloration of the surface region 404 of the object 428. Scatterguards of other colors and colorations are also contemplated. In thisembodiment, the scatter guards 432 have a height that is lower than theheight of the first and second material regions 406 and 408. Having ascatter guard 432 with a lower height than the colored regions in anobject enables the scatter guard to limit the scattering that occurs inthe transparent material 412 without significantly obstructing thevisibility of the sides of the colored regions from the perspective ofobservers viewing the surface region 404 at an oblique angle.

FIG. 5 illustrates another exemplary embodiment of a three-dimensionalobject 500 that includes arrangements 514 that are similar to thearrangements 414 in FIGS. 4A and 4B. Each arrangement 514 also includesa first material region 406 and a second material 408 that overlap in adirection parallel to the surface region 501. However, each arrangement514 further includes a third material region 502 that is white. A firstportion 504 of the third material region 502 is disposed between thefirst material region 406 and second material region 408 and acts as abuffer to inhibit bleed-through. A second portion 506 of the thirdmaterial region 502 is disposed on a side of the first material region406 and second material region 408 facing toward a surface 503 of thesurface region 501. The second portions 506 of the third materialregions 502, together with transparent material regions 412 define thesurface region 501.

In this configuration, the white third material region 502 does notobstruct the portions of the first material region 406 and secondmaterial region 408 facing toward the transparent material regions 412from view. Thus, to the first observer 418, primarily white from thethird material region 502 and yellow from the first material region 406are visible, and to the second observer 420, primarily white from thethird material region 502 and cyan from the second material region 408are visible. Furthermore, due to the second portion 506 of the thirdmaterial region 502, as the view angle moves toward the 90 degreesperspective of a third observer 508, the apparent coloration of thesurface region 501 moves toward white. In other embodiments (not shown)the third material region 502 can have different colors or combinationsof colors. In another embodiment (not shown) the object 500 furtherincludes a scatter guard disposed within the transparent material region412 similar to the scatter guard 432 illustrated in FIG. 4B. The readershould also understand that while FIGS. 4A, 4B, and 5 illustratetwo-dimensional cross-sections of three-dimensional objects 400 and 500,the arrangement of material regions can extend into a third dimension.

FIG. 6 illustrates a top view of several exemplary arrangements ofmaterial regions that have different apparent colors not only from aleft view direction and a right view direction, but also from a frontview direction and rear view direction, or more. As illustrated in FIG.6, differently colored material regions can be arranged in both regularand irregular shapes and with different numbers of colored materialregions to achieve different coloration behaviors. The examples of FIG.6 include a pyramid 604 having different colors on its faces, a rightcylinder 608 divided into sectors having different colors, and anirregular three-dimensional shape 612 composed of different coloredsegments. Because the apparent coloration of a surface region due to thearrangements illustrated in FIG. 6 are different for a multitude ofdifferent view directions, such arrangements enable surface regions tohave a coloration that changes with rotation of an object. As the objectrotates, different sides of the arrangements are exposed to the viewerin different proportions, and thus the apparent coloration of the objectto the viewer changes.

In the above embodiments, various observers are described as viewing thesurface region of a three-dimensional object under, for example,generally diffuse light that is uniform regardless of view direction orview angle. However, a similar effect with a changing apparentcoloration of the surface region of the three-dimensional object can beachieved with a stationary observer and a changing focused source ofillumination, i.e., with illumination lighting the surface region atdifferent angles. In other words, if the observers discussed above arereplaced with focused illumination sources, at least a substantialportion of the light reflecting off of or transmitted from thethree-dimensional object corresponds with the proportions of thematerial regions illuminated by the light from the illumination sources.This illumination results in an apparent coloration of the surfaceregion of the three-dimensional object without regard for a location ororientation of the viewer.

In another example, a similar coloration changing effect can be achievedusing non-focused illumination. For instance, the sun provides generallydiffuse light at an orientation that changes throughout the course of aday. A three-dimensionally printed object according to this disclosurecan be configured to exhibit a coloration that changes based on anorientation of the sun. In other words, given a fixed perspective of anobserver viewing an object, relative motion between the observer, theobject, and the illumination source can be used to cause colorationchanges according to this disclosure.

In some embodiments, a three-dimensional object according to thisdisclosure may include internal illumination. Such illumination may bedue to, for example, a light source disposed within the object, due tophosphorescence, or due to light transmitted into the object, such as aback-light. Changes in apparent coloration of a surface region viafocused internal illumination can operate in a similar fashion toexternal focused illumination. In an example, internal illumination isproduced within a three-dimensional object that is generally oriented ina first view direction. A substantial portion of the light that isemitted from the three-dimensional object is emitted along the firstview direction and is emitted from the portions of the material regionsvisible along a second view direction opposite the first view direction.As a result, the apparent coloration of the surface region may bealtered by changing the direction of the internal illumination.

In embodiments where illumination of the object is at least generallyexternal, colors for the plurality of differently colored materialregions advantageously includes cyan, magenta, yellow, black, white,reflective, and at least partially transparent. Conversely, inembodiments where illumination of the object is at least generallyinternal, colors for the plurality of differently colored materialregions advantageously includes red, green, blue, black, white,reflective, and at least partially transparent. In other words, thecolor selection for the materials follows the principles of additive andsubtractive coloration for various forms of illumination.

FIG. 7A illustrates yet another embodiment of a three-dimensional object700 according to this disclosure. The object 700 includes arrangements718, each of which has a first material region 706, a second materialregion 708, a third material region 710, a fifth material region 714,and a sixth material region 716. The object 700 further includes a base718 that supports the first material regions 706 and second materialregions 708, and a fourth material region 712 that supports the thirdmaterial region 710, fifth material region 714, and sixth materialregion 716. The fourth material region 712 additionally encapsulates thematerial regions 706, 708, 710, 714, and 716, and defines a surfaceregion 704 of the object 700 having a surface 705. The material regions706-716 are collectively referred to as a plurality of material regions702. The arrangements 718 combine the principles of various arrangementsdiscussed in the other embodiments above. Other combinations are alsocontemplated. Such combinations enable the formation ofthree-dimensional objects with surface regions that have a changingcoloration over both view and illumination angles and view directions.

In the embodiment of FIG. 7A, the first material region 706 is yellow,the second material region 708 is cyan, the third material region 710 ismagenta, the fourth material region 712 is at least partiallytransparent, the fifth material region 714 is white, the sixth materialregion 716 is black, and the base 718 is white. In other embodiments,other colors and combinations of colors are also contemplated. In thearrangements 718, the first material region 706 and second materialregion 708 are disposed on the base 718, with the second material region708 that overlaps with the first material region 706 in a directiongenerally parallel to the surface 705. The third material region 710 isspaced apart from the first material region 706 and second materialregion 708 in a direction toward the surface 705. At least a portion ofthe fourth material region 712 is disposed between the third materialregion 710 and the first and second material regions 706 and 708. Thefifth material region 714 is disposed on a side of the third materialregion 710 facing away from the surface 705 and toward the first andsecond material regions 706 and 708. The sixth material region 716 isdisposed on a side of the fifth material region 714 facing away from thethird material region 710 and toward the first and second materialregions 706 and 708. The base 718 is further configured to act as abuffer to inhibit bleed-through between, for example, the surface region704 and a surface region 720 of the object 700. The fifth materialregion 714 is also configured as a buffer to inhibit bleed-throughbetween the third material region 710 and the first and second materialregions 706 and 708. The sixth material region 716 is configured as ascatter guard.

From the perspective of a first observer 722 viewing the surface regionat approximately a 90 degree angle, the only portions of the materialregions that are visible are the magenta of the third material region710 and the white from the base 718. Thus, the surface region 704 has anapparent coloration that is light magenta. From a perspective of asecond observer 724 viewing the surface region at an oblique angle andat a view direction facing toward the right, the magenta from the thirdmaterial region 710, the cyan from the second material region 708, andthe white from the base 718 are visible, and the surface region has anapparent coloration that is generally light blue. As the angle becomesmore oblique more of the cyan from the second material region 708becomes visible, and the surface region 704 appears bluer. Furthermore,at a highly oblique angle, yellow from a portion of the first materialregion 706 may become visible, and thus the surface region 704 appearsto be a darker blue. From a perspective of a third observer 726 viewingthe surface region at an oblique angle and at a view direction facingtoward the left, the magenta from the third material region 710, theyellow from the first material region 706, and the white from the base718 are visible so the surface region has an apparent coloration that isgenerally light red. As the angle becomes more oblique more of theyellow from the first material region 706 becomes visible, and thesurface region 704 appears redder. Furthermore, at a highly obliqueangle, cyan from a portion of the second material region 708 may becomevisible, and the surface region 704 appears to be a darker red.

FIG. 7B illustrates a further exemplary embodiment of athree-dimensional object 730 that is similar to the object 700 in FIG.7, except the scatter guards 716 have been replaced with alternativescatter guards 732. The alternative scatter guards 732, like the scatterguards 716 in FIG. 7A, are disposed on a side of the fifth materialregion 714 facing away from the third material region 710 and toward thefirst and second material regions 706 and 708. The alternative scatterguards 732 additionally extend toward, and in particular make contactwith, the first and second material regions 706 and 708. In thisembodiment, the alternative scatter guards 732 are defined by agenerally T-like shape, but other shapes are also contemplated in otherembodiments. The alternative scatter guards 732 are configured tovisibly separate the first and second material regions 706 and 708, suchthat observers viewing the surface region 704 do not have visibility ofboth of the first and second material regions 706 and 708. Ensuring thatonly one of the first and second material regions 706 and 708 is visibleto an observer at a time can reduce blending of the different colors ofthe different material regions. In this embodiment, the alternativescatter guards 432 are gray, but other colorations and combinations ofcolorations are also contemplated. Using a gray material for thealternative scatter guards can limit a darkening effect of thecoloration of the surface region 704 from perspectives where thealternative scatter guards 432 are visible.

FIG. 8 illustrates another exemplary embodiment of a three-dimensionalobject 800 according to this disclosure. The object 800 is similar tothe object 700 illustrated in FIG. 7A, but the positions of the thirdmaterial region 710 and the first and second material regions 706 and708 in arrangements 818 have been swapped relative to their positions inarrangements 718 in FIG. 7. As a result, a first observer 802 views thesurface region 804 as a mixture of cyan and yellow, i.e., green. Asecond observer 806 viewing in a direction facing toward the right seesthe surface region as a mixture of cyan and magenta, i.e., blue. A thirdobserver 808 viewing in a direction facing toward the left sees thesurface region as a mixture of yellow and magenta, i.e., red.

In a further embodiments (not shown), the object 800 can additionallyinclude buffer regions between the first and second material regions 706and 708 similar to the buffer regions 430 in FIG. 4B, and canadditionally include scatter guards between the arrangements 818 similarto the scatter guards 432 in FIG. 4B. In further embodiments, thedifferent arrangements and configurations described in the variousembodiments above are combined, modified, and reoriented in order toform different coloration behaviors for a three-dimensionally printedobject. Based on the foregoing arrangements of differently coloredmaterial regions, surface regions can be formed that appear to havedifferent colorations for a variety of view angles, view directions, andillumination angles.

While the objects illustrated in FIGS. 1-8 appear to have a generallyregular shape, irregular three-dimensional objects are alsocontemplated. FIG. 9A illustrates a cross sectional view of an exemplaryembodiment of an irregular three-dimensional object 900 according tothis disclosure that incorporates various features from the foregoingembodiments. The reader should understand that the object 900 may extendin an irregular fashion in the third dimension as well. In this fashion,surface regions with complex coloration behaviors can be formed.

FIG. 9B is a schematic illustrating how different images 902 and 904 areused to form an exemplary embodiment of a three-dimensionally printedobject 910 according to this disclosure having a coloration that changesbetween the different images 902 and 904 based on a perspective at whichthe object 910 is viewed. FIG. 9C illustrates a side cross section viewof a detail region 906 of the object 910. The reader should understandthat the depiction of the object 910 in FIGS. 9B and 9C is symbolic, andis not an accurate representation of the surface coloration of athree-dimensionally printed object according to this disclosure. Inaddition to not being drawn to scale, FIGS. 9B and 9C aretwo-dimensional images, and therefore are two-dimensional drawings thatsymbolize the three-dimensional viewing behaviors of objects printedaccording to this disclosure.

As shown in FIG. 9C, the object 910 is formed from a plurality ofdifferently colored material regions 912 that include a first subset ofmaterial regions 914 and a second subset of material regions 916. Thefirst subset of material regions 914 correspond to the first image 902.In other words, if the first subset of material regions 914 were viewedin isolation, the material regions would have a coloration that formsthe first image 902. Similarly, the second subset of material regions916 corresponds to the second image 904, and if viewed in isolationwould have a coloration that forms the second image 904.

The plurality of material regions 912 is arranged such that when theobject 910 is viewed from a first view angle, e.g., from a generallyvertical angle, the first subset of material regions 914 and thus thefirst image 902 is primarily visible. The plurality of material regions912 is further arranged such that when the object 910 is viewed from asecond view angle, e.g., from a generally oblique angle, the secondsubset of material regions 916 and, consequently, the second image 904is primarily visible. In this embodiment, the arrangement of theplurality of material regions 912 includes a base layer 918 that iswhite, an interlaced arrangement 920 of the first and second subsets ofmaterials 914 and 916 disposed on the base layer 918, a transparentmaterial region 922 disposed on top of the arrangement 920, andnon-transparent regions 924 spaced apart from the arrangement 920 by thetransparent material region 922. In this embodiment, the non-transparentmaterial regions 924 are black, but other colorations and combinationsof colorations are also contemplated in other embodiments. The blackmaterial regions 924 are arranged so as to at least partially overlapthe second subset of material regions 916 in the vertical direction. Asa result, to an observer viewing the object 910 from a generallyvertical direction, the black material regions 924 at least partiallyobscure the second subset of material regions 916 from view whileenabling visibility of at least a portion of the first subset ofmaterial regions 914 so that the first image 902 is primarily visible.Conversely, to an observer viewing the object 910 from an obliquedirection, the black material regions 922 obscure at least a portion ofthe first subset of material regions 914 and enable visibility of atleast a portion of the second subset of material regions 916 so that thesecond image 904 is primarily visible.

Although the images 902 and 904 are illustrated as being differentimages, e.g., a smiling face and a heart respectively, in otherembodiments, the second image 904 could be a modification of the firstimage 902. For instance, the first image 902 could be a smiling face andthe second image 904 could be a frowning face. In other examples, thesecond image 904 can illustrate an object from the first image 902 in adifferent position or perspective, with a different color, brightness,intensity, or with an additional optical illusion. An “optical illusion”as used herein means a visual image that, when perceived by a humanobserver, appears to include features not physically consistent oractually present in the visual image.

Additionally, while the coloration behavior of the object 910 was formedusing the arrangement of the plurality of material regions 912 describedabove, other arrangements that incorporate the techniques described inthis disclosure can be used to form similar coloration behaviors inother embodiments. Furthermore, while the object 910 incorporates twodifferent images 902 and 904, three-dimensionally printed objectsaccording to this disclosure can incorporate any number of images thatare visible from any number of view angles, view directions, andillumination directions.

The arrangement of differently colored material regions that enablesdifferent colorations on a surface region of a three-dimensional objectmay be complex. This complexity may be exacerbated when the surfaceregion of the three-dimensional object has an irregular shape and whenthe coloration has a high level of detail or color variation. Therefore,a technique for modifying a three-dimensional object to have a pluralityof differently colored material regions that form a surface region witha desired iridescent coloration behavior would be beneficial. As usedherein, “modify” means to change or replace, at least in part, so as toexhibit different structure or behavior, specifically with regard to anarrangement of different material regions within a three-dimensionalobject.

FIG. 10B illustrates an exemplary embodiment of a system 1050 configuredto perform the method 1000 illustrated in FIG. 10A in order to producean iridescent three-dimensional object by modifying three-dimensionaldata for printing the three-dimensional object so that thethree-dimensional object has a surface region having different colorarrangements visible to an observer viewing the surface region fromdifferent view directions, different view angles, and with illuminationlighting the surface region at different angles. As shown in FIG. 10B,the system 1050 includes a memory 1052, an input device 1054, aprocessor 1056, and an output device 1058, which are interconnected by asystem bus 1060.

Three-dimensional data for operating a three-dimensional printer isstored on the memory 1052. For example, the three-dimensional data mayinclude data describing a three-dimensional geometry of an object to beprinted, printing layer data, object material data, or other data thatenables the three-dimensional printer to print a three-dimensionalobject.

The input device 1054 is configured to receive data corresponding to atleast two different color arrangements for the surface region of thethree-dimensional object, and data corresponding to at least one of aview direction, a view angle, and an illumination angle assigned to eachdifferent color arrangement. In another embodiment, the input device1054 is further configured to receive the three-dimensional data andstore the three-dimensional data in the memory 1052. The input devicecan also be configured to receive other information, such as userinstructions pertaining to, for example, a predetermined threshold formeasuring a similarity between the coloration of the different colorarrangements and the resulting modified three-dimensional object.

The processor 1056 is configured with programmed instructions stored inthe memory 1052 that enable the processor 1056 to modify thethree-dimensional data to enable the three-dimensional object to beformed with different color arrangements visible to an observer viewingthe surface region from different view directions, different viewangles, and with illumination lighting the surface region at differentangles. The processor 1056 is thus configured to perform the followingacts, illustrated in FIG. 10A, and the output device 1058 is configuredto output the modified three-dimensional data to the three-dimensionalobject printer.

A color change map for the surface region of a three-dimensional objectis generated (block 1004). As used herein, “generate” means to producevia an algorithm, predetermined instructions, or via a mathematicalprocess using input information. The color change map describes thecoloration of the surface region from various view directions, viewangles, and illumination angles, and is determined with reference to aportion of the three-dimensional data corresponding to a geometry of thesurface region of the three-dimensional object, the data received by theinput device that corresponds to at least two different colorarrangements for the surface region, and the data received by the inputdevice that corresponds to the at least one of the view direction, theview angle, and the illumination angle assigned to each different colorarrangement. The geometry of the surface region describes thethree-dimensional shape of the surface region of the object. Forexample, a geometry could define the surface region of a cube, a sphere,or any other regular or irregular three-dimensional shape. Colorarrangements refer to a particular coloration for the surface regionthat is visible from the assigned view angle, view direction, orillumination angle for the generated map. For example, colorarrangements for an object could include blue text with a greenbackground from the left and yellow text with a red background from theright. Other examples for color arrangements include images, opticalillusions, stereoscopic images, animations with different componentimages at different view points, or any other acceptable type ofcoloration. Each color arrangement is assigned with a particular viewdirection, view angle, and illumination angle. Together, the geometry,color arrangements, and view angles, view directions, and illuminationangles describe the desired coloration behavior for the surface regionof the object.

The process 1000 continues with the generation of a model of the objectwith reference to the map (block 1008). As used herein, “model” means animitative or schematic representation of a three-dimensional elementthat can be used to examine properties of the element. The modelincludes data corresponding to a plurality of different material regionsthat together define a model surface region of the model. The pluralityof different material regions overlap by different amounts viewed fromdifferent directions such that different proportions of light from thedifferent material regions are visible to an observer viewing the modelsurface region from different view angles, different view directions,and with illumination lighting the model surface region at differentangles. The model surface region roughly corresponds to the surfaceregion of the three-dimensional object. In other words, while theinternal geometry of the plurality of material regions within the modeldiffers from the geometry of the three-dimensional object, the outergeometry of the model that defines the shape of the model generallycorresponds with the shape of the three-dimensional object. Theplurality of material regions within the model can be arranged randomly,or can be arranged with reference to at least one of the colorarrangements.

A view of the surface region of the model from an observer is thensimulated for each of the view angles, view directions, and illuminationangles assigned to the various color arrangements (block 1012). As usedherein, “simulate” means to enact a representation of a system, inparticular of the surface region of the model, in order to predict abehavior or property of the system.

Based on the simulation, a proportion of light from each of theplurality of material regions visible to the observer at each assignedview direction, view angle, and illumination angle is identified (block1016). As used herein, “identify” means to ascertain as having a certaincharacteristic or feature via an algorithm, predetermined instructions,or mathematical process that provides a numerical result with referenceto the feature or characteristic. Since the different proportions oflight from differently colored material regions visible at a portion ofa surface region defines an apparent coloration of that portion of thesurface region, the simulated proportions of visible light from materialregions can then be used to form a color change map for the surfaceregion of the model (block 1020).

The color change map of the surface region of the model is compared tothe color change map of the surface region of the desiredthree-dimensional object to measure a similarity of at least one ofcolor hue and color location between the generated color map of themodel and the generated color map of the three-dimensional object (block1024). If they match, i.e., if the measured similarity is greater than apredetermined threshold at the at least one of the assigned viewdirection, view angle, and illumination angle, then the model hasachieved an arrangement of material regions that enables the desiredcoloration behavior (block 1028). The threshold for the measuredsimilarity can describe, for example, a predetermined percentage of themodel surface region that, when viewed in each of the assigned viewangles, view directions, and illumination angles, has a colorationcorresponding to the desired coloration of the surface region. Thethreshold can also describe a predetermined hue similarity between acolor or colors visible on the model surface region and the surfaceregion of the desired object. If the color change map of the modelsurface region does not match the color change map of the surface regionof the desired three-dimensional object, i.e., is outside of thepredetermined threshold of similarity, then the arrangement of thematerial regions in the model and the simulation of the views areiterated (blocks 1008-1020) until the map of the surface region and themap of the model sufficiently match (block 1024). In an example, anobject is desired to appear blue from a perspective perpendicular to asurface region, and green from a perspective to the left of the surfaceregion. An initial model is formed that appears blue from both the leftand from the perpendicular view in simulated views. The arrangement ofmaterial regions in the model can then be adjusted until the desiredappearance is achieved within the predetermined threshold of similarity.

The reader should understand that different materials have differentoptical properties that limit the coloration behavior of the materialsat different view angles, view directions, and illumination angles. Forexample, an amount of transparency, scattering, absorption, or otherproperties of a material may limit a range of coloration for thematerial at certain view angles, view directions, and illuminationangles. Additionally, such properties can affect how different materialsinteract when positioned proximate to each other. This interaction mayexacerbate the difficulty in achieving a color change map of the surfaceregion of the model that is within the threshold of similarity with thecolor change map of the desired three-dimensional object. In oneembodiment, the color map of the desired three-dimensional object isadjusted so as to be limited to a predetermined selection of colors. Inanother embodiment, the threshold for similarity is increased inresponse to a determination that the desired color map is outside therange of coloration enabled by the materials available for printing. Ina further embodiment, the color map for the desired object is adjustedto prioritize a change in coloration over different perspectives even ifthe resulting colors of the coloration do not match. For example, adesired object includes a coloration that changes from pink to greenover two different perspectives. Given the available materials, a changefrom orange to green may not be possible over the two assignedperspectives. The color change model of the desired object is changed tobe a color change from red to green instead of orange to green so that acoloration change of the desired magnitude occurs even if the precisecolors of the change are different. In yet another embodiment, the colorchange map of the desired object is adjusted to prioritize a particularcoloration behavior, such as a change over a particular view angle orview direction. In an embodiment, the colors in the coloration behaviorsof the color change map of the desired object are adjusted to be aclosest matching color within the range of colors enabled by theavailable materials.

In an example of the iteration of the color change map of the model, aninitial model may include an arrangement similar to arrangement 116 inFIG. 1. In an iteration, the arrangement 116 could be replaced with adifferent arrangement, such as the arrangement 414 in FIG. 4.Adjustments within an iteration can also include adjusting a color of amaterial region, adjusting a size of a material region, adjusting aspacing between adjacent material regions, adjustments of a shape of abase region, buffer region, or scatter guard region, or any otheracceptable adjustments. The views of the model can then be re-simulatedto determine if the desired coloration behavior is achieved. Once themodel accurately describes an arrangement of material regions thatenables the desired coloration behavior, the model is used to modify thethree-dimensional data for printing the three-dimensional object (block1026). The modified three-dimensional data is then transmitted to athree-dimensional object printer (block 1028), that uses the modifieddata to print the object so as to have surface region having acoloration behavior defined by the different color arrangements at theassigned view angles, view directions, and illumination angles (block1030).

In one embodiment, the system 1050 is integrated with a controller of athree-dimensional object printer. In another embodiment, the system 1050is separate from the three-dimensional object printer, and can beconfigured to communicate with the printer via, for example, anelectronic signal such as a signal transmitted via a network or signalline, via a disk, drive, or other portable computer-readable memory, viainstructions communicated to a user, or the like. Additionally, whileFIG. 10A illustrates a single processor 1056, the reader shouldunderstand that the system 1050 can be implemented with more than oneprocessor and associated circuitry and components, each of which isconfigured to form one or more tasks or functions described herein.

FIG. 11 illustrates an exemplary embodiment of a three-dimensionalobject printer 1100 for printing a three-dimensional object 1102according to this disclosure. The printer 1100 includes a firstplurality of ejectors 1104, a second plurality of ejectors 1106, and acontroller 1108. The first plurality of ejectors 1104 is operable toeject drops of material having a first color and the second plurality ofejectors is operable to eject drops of material having a second colordifferent from the first color. The controller 1108 is configured tomove (i) the first plurality of ejectors 1104 and second plurality ofejectors 1106, and (ii) the object 1102 relative to each other. Thecontroller 1108 is also configured to operate the first plurality ofejectors 1104 and second plurality of ejectors 1106 to eject materialand form first material regions 1110 and second material regions 1112respectively, in order to form the object 1102. Other components andaspects of the printer 1100 are not included in detail for the purposeof clarity. The object 1102 and printer 1100 are not drawn to scale, andadditional elements, such as support structures, actuators, and othercomponents of a three-dimensional object printer known to those of skillin the art are not shown in FIG. 11.

In one embodiment, the controller 1108 operates the first plurality ofejectors 1104 and second plurality of ejectors 1106 to eject drops ofmaterial to form layers that gradually build together to form athree-dimensional object. In other words, each of the first plurality ofejectors 1104 and second plurality of ejectors 1106 form any firstmaterial regions 1110 and 1112 in the current layer before beginning toform a subsequent layer. In this fashion, successive layers of materialare ejected to form the three-dimensional object layer by layer.

In another embodiment, the controller 1108 operates the first pluralityof ejectors 1104 to fully form a first material region 1110, and thenthe second plurality of ejectors 1106 is operated to form a secondmaterial region 1112. In other words, the object 1102 is formed regionby region, rather than layer by layer, where each individual region isformed layer by layer.

Those skilled in the art will recognize that numerous modifications canbe made to the specific implementations described above. Therefore, thefollowing claims are not to be limited to the specific embodimentsillustrated and described above. The claims, as originally presented andas they may be amended, encompass variations, alternatives,modifications, improvements, equivalents, and substantial equivalents ofthe embodiments and teachings disclosed herein, including those that arepresently unforeseen or unappreciated, and that, for example, may arisefrom applicants/patentees and others.

1-13. (canceled)
 14. A method of operating a printer to produce athree-dimensionally printed object comprising: receivingthree-dimensional data that defines a geometry of a surface region ofthe three-dimensionally printed object, at least two different colorarrangements for the surface region, and at least one of a viewdirection, a view angle, and an illumination angle assigned to eachdifferent color arrangement; generating a model of thethree-dimensionally printed object that includes data corresponding to aplurality of different material regions that together define a modelsurface region of the model and that overlap by different amounts viewedfrom different directions to enable different proportions of light fromthe plurality of different material regions to be visible to an observerviewing the model surface region from at least one of different viewdirections, different view angles, and with illumination lighting thesurface region at different angles such that a coloration of the modelsurface region viewed from the view directions, view angles, andillumination angles defined by the three-dimensional data corresponds tothe at least two color arrangement to which the view directions, viewangles, and illumination angles are assigned; generating a color changemap for the surface region with reference to the geometry of the surfaceregion, the at least two different color arrangements for the surfaceregion, and the at least one view direction, view angle, andillumination angle assigned to each different color arrangement;generating a color change map of the model surface region with referenceto the data corresponding to a plurality of different material regionsthat together define the model surface region and the at least one viewdirection, view angle, and illumination angle assigned to each differentcolor arrangement; comparing the color change map of the surface regionto the color change map of the model surface region to measure asimilarity of at least one of color hue and color location between thecolor change map of the surface region to the color change map of themodel surface region; continuing the generation of the model until themeasured similarity between the color change map of the surface regionto the color change map of the model surface region is greater than apredetermined threshold at the at least one view direction, view angle,and illumination angle assigned to each different color arrangement;modifying the geometry of the surface region of the three-dimensionallyprinted object with reference to the generated model; operating withreference to the modified geometry of the surface region a first subsetof the plurality of ejectors that eject drops of a material having afirst color to form a first material region of the first color; andoperating with reference to the modified geometry of the surface regiona second subset of the plurality of ejectors that eject drops of amaterial having a second color that is different than the first color toform a second material region of the second color, the plurality ofdifferent material regions overlapping each other by different amountsviewed from different directions to enable different proportions oflight from the plurality of different material regions to be visible toan observer viewing the surface region of the three-dimensionallyprinted object from at least one of different view directions, differentview angles, and with illumination lighting the surface region atdifferent angles, and to enable a coloration of the surface region ofthe three-dimensionally printed object to be altered based on theproportions of light the first material region and second materialregion visible to the observer.
 15. The method according to claim 14,wherein second colored material region and the first colored materialregions are at different distances from a surface of the surface region.16. The method according to claim 15, the operation of the plurality ofejectors to form the plurality of different material regions furthercomprising: operating a third subset of the plurality of ejectors thateject drops of material having a third color that is transparent to forma third material region that is transparent, the third material regionbeing positioned between the first material region and the secondmaterial region relative to the surface; and operating a fourth subsetof the plurality of ejectors that eject drops of material that is whiteto form at least one fourth material region that is white, the at leastone fourth material region being positioned on a side of at least one ofthe first material region and the second material region facing awayfrom the surface.
 17. The method according to claim 16, the operation ofthe plurality of ejectors to form the plurality of different materialregions further comprising: operating a fifth subset of the plurality ofejectors that eject drops of material that is black to form a fifthmaterial region that is black and that is positioned between the firstmaterial region and the third material region relative to the surface.18. The method according to claim 14, wherein the second material regionoverlaps with the first material region in a direction generallyparallel to a surface of the surface region.
 19. The method according toclaim 14, the operation of the plurality of ejectors to form theplurality of different material regions further comprising: operatingthe plurality of ejectors to form a first subset of material regionsthat form an image on the surface region over at least one of a firstview direction, a first view angle range, and a first illumination anglerange; and operating the plurality of ejectors to form a second subsetof material regions modifying the image formed on the surface by thefirst plurality of material regions over at least one of a second viewdirection, a second view angle range, and a second illumination range.20-21. (canceled)
 22. The method of claim 14 further comprising:simulating a view of an observer viewing the model surface region at theat least one view direction, view angle, and illumination angle assignedto each different color arrangement; and identifying differentproportions of light from the different material regions that arevisible to the observer from the at least one of the view direction, theview angle, and the illumination angle assigned to each different colorarrangement with reference to the simulated view of the observer, thecolor change map of the model surface region being generated withfurther reference to the identified proportions of light from eachmaterial region visible to the observer from the at least one of theview direction, the view angle, and the illumination angle assigned toeach different color arrangement.
 23. The method of claim 22, whereinthe continuation of the generation of the model includes: for eachgeneration of the model, continuing the simulation of the view of anobserver viewing the model surface region, the identification ofdifferent proportions of light from the different material regions thatare visible to the observer, and the comparison of the color change mapof the surface region to the color change map of the model surfaceregion.
 24. A method of operating a three-dimensional object printer toproduce a three-dimensionally printed object with a surface region thathas different color arrangements visible to an observer viewing thesurface region from different view directions, different view angles,and with illumination lighting the surface region at different angles,the method comprising: providing three-dimensional data that defines ageometry of a surface region of the three-dimensionally printed object,at least two different color arrangements for the surface region, and atleast one of a view direction, a view angle, and an illumination angleassigned to each different color arrangement; generating a model of thethree-dimensionally printed object that includes data corresponding to aplurality of different material regions that together define a modelsurface region of the model and that overlap by different amounts viewedfrom different directions to enable different proportions of light fromthe plurality of different material regions to be visible to an observerviewing the model surface region from at least one of different viewdirections, different view angles, and with illumination lighting thesurface region at different angles such that a coloration of the modelsurface region viewed from the view directions, view angles, andillumination angles defined by the three-dimensional data corresponds tothe at least two color arrangement to which the view directions, viewangles, and illumination angles are assigned; generating a color changemap for the surface region with reference to the geometry of the surfaceregion, the at least two different color arrangements for the surfaceregion, and the at least one view direction, view angle, andillumination angle assigned to each different color arrangement;generating a color change map of the model surface region with referenceto the data corresponding to a plurality of different material regionsthat together define the model surface region and the at least one viewdirection, view angle, and illumination angle assigned to each differentcolor arrangement; comparing the color change map of the surface regionto the color change map of the model surface region to measure asimilarity of at least one of color hue and color location between thecolor change map of the surface region to the color change map of themodel surface region; continuing the generation of the model until themeasured similarity between the color change map of the surface regionto the color change map of the model surface region is greater than apredetermined threshold at the at least one view direction, view angle,and illumination angle assigned to each different color arrangement;modifying the geometry of the surface region of the three-dimensionallyprinted object with reference to the generated model; and operating athree-dimensional object printer with reference to the modified geometryto produce the three-dimensional object.
 25. (canceled)
 26. The methodof claim 24 further comprising: simulating a view of an observer viewingthe model surface region at the at least one view direction, view angle,and illumination angle assigned to each different color arrangement; andidentifying different proportions of light from the different materialregions that are visible to the observer from the at least one of theview direction, the view angle, and the illumination angle assigned toeach different color arrangement with reference to the simulated view ofthe observer, the color change map of the model surface region beinggenerated with further reference to the identified proportions of lightfrom each material region visible to the observer from the at least oneof the view direction, the view angle, and the illumination angleassigned to each different color arrangement.
 27. The method of claim26, wherein the continuation of the generation of the model includes:for each generation of the model, continuing the simulation of the viewof an observer viewing the model surface region, the identification ofdifferent proportions of light from the different material regions thatare visible to the observer, and the comparison of the color change mapof the surface region to the color change map of the model surfaceregion. 28-31. (canceled)